Predictor-based sampled-data stabilization via continuous-discrete observers

We consider a stabilization problem for a continuous-time linear system with discrete-time measurements and a sampled input with a pointwise constant delay. In a first step, we construct a continuous-discrete observer which converges when the maximum time interval between two consecutive measurements is sufficiently small. In a second step, we construct a dynamic output feedback through a technique which is strongly reminiscent of the reduction model approach. It stabilizes the system when the maximal time between two consecutive sampling instants is sufficiently small. No limitation on the size of the delay is imposed.